Question

Please help me solve for x , and indentify if its extraneous.
square root only over over x-95 ,+9 = 6

Answer 1

\[\sqrt{x-95}+9=6\]?

Answer 2

Yes

Answer 3

You're sure about that?

Answer 4

yes because my teacher is asking me to substitute my birth date and year into this equation

Answer 5

\[\sqrt{x-95}= -3\]

Answer 6

square both sides

Answer 7

oh okay. so that's what I start with?

Answer 8

Problem is that there's no real solution…

\[\sqrt{x-95}+9=6\]\[\sqrt{x-95}=-3\]There's no real number that satisfies that...

Answer 9

x-95=9 and yess

Answer 10

now just add 95 on both sides

Answer 11

okay so maybe ill just tell her to screw,and I cant do it.yay.

Answer 12

Maybe that's what your instructor hopes you'll find...

Answer 13

ok hold on, let me attempt this

Answer 14

you get x=92

Answer 15

I got x = 104?

Answer 16

ooops yes you are correct

Answer 17

hallelujah

Answer 18

i was looking at the previous forms of this equation

Answer 19

thank you gentlemen for your help

Answer 20

nice! no problem

Answer 21

you aren't done yet, though — you need to test out your solution to see if it works.

Answer 22

oh no

Answer 23

\[\sqrt{104-95} +9 = 6\]Can you simplify that?

Answer 24

let me see

Answer 25

@whpalmer4 thats right, forgot about that. good thing we are both here

Answer 26

lol

Answer 27

ok I got 9=9 at the end

Answer 28

so I hope im right

Answer 29

no, you don't get that…
what is the value of the square root?

Answer 30

uhm, im not sure

Answer 31

then how could you know that you got the right thing?

Answer 32

\[\sqrt{104-95} = \]

Answer 33

u get \[\sqrt{9}=6\]

Answer 34

or just 3

Answer 35

okay, so I minused 104 from 95,
got 9 plus 9 = 6 then I squared both and took 9 out of the square root

Answer 36

then I did 6-9 which is -3 but squared is 9 so I got 9=9

Answer 37

ohhhh no shes right

Answer 38

it can be plus or minus 3

Answer 39

or realy

Answer 40

+3+9=6 is wrong but
-3+9=6

Answer 41

* oh really

Answer 42

ok well good deal

Answer 43

no, without a sign in front of the radical, it means the principal root, which is the positive one.

Answer 44

leaving us with \[3+9=6\]

Answer 45

hm

Answer 46

INSTEAD OF SQUARING BOTH SIDES SHE CAN SIMPLIFY THE SQUARE ROOT OF 9 with = plus or minus 3

Answer 47

*which

Answer 48

so x=104 is an extraneous solution.

we introduced it when we squared both sides of the equation.

Answer 49

only \[-\sqrt{x-95}+9=6\]has a solution

Answer 50

I thought it is only extraneous if theres a negative sign in front.

Answer 51

oh.

Answer 52

are you sure @whpalmer4

Answer 53

Go watch this video: http://www.khanacademy.org/math/algebra/exponent-equations/radical_equations/v/extraneous-solutions-to-radical-equations

Answer 54

okay

Answer 55

110% sure.

Answer 56

http://www.wolframalpha.com/input/?i=sqrt%28x-95%29%2B9%3D6

Answer 57

no, extraneous means "it doesn't work" :-)

Answer 58

im already lost at 1:43

Answer 59

I don't understand why theres a -24x

Answer 60

\[(2x-6)(2x-6) = 2x*2x-6*2x-6*2x+36 = 4x^2-24x+36\]